Trapped symmetric disturbances in rotating shear flows

The structure of trapped symmetric disturbances in rotating stratified shear flows is investigated theoretically. It is shown that the arrangement of the trapping region is determined by atmospheric stratification. For example, if the characteristic Brunt-Väisälä frequency is greater (smaller) than the inertial frequency, waves are trapped in the region of anticyclonic (cyclonic) velocity shear. Accordingly, in the first (second) case, the frequencies of trapped waves are smaller (greater) than the inertial frequency. The problem of finding the frequencies of trapped waves is reduced to solving the Schrödinger equation but with a more complex dependence on a spectral parameter. Exact solutions to the problem are obtained for a triangular jet and a hyperbolic shear layer.     

Trapped quasi-inertial waves in shear oceanic currents

We studied trapped long quasi-inertial waves in horizontally inhomogeneous flows with low Rossby numbers. A simple heuristic derivation of two equations for the wave amplitude is presented. These equations are true for strong and weak density stratifications. A spectral problem is formulated to find the frequencies of trapped waves based on the amplitude equations. Exact solutions of the hyperbolic problem for a free hyperbolic shear layer are found. It is shown that the location of the trapping area principally depends on the stratification. If the buoyancy frequency is greater than the inertial frequency, trapping occurs in the region of anticyclonic velocity shear; if the buoyancy frequency is smaller than the inertial frequency, trapping occurs in the region of cyclonic velocity shear. Thus, in the first case, the frequencies of the trapped waves are smaller than the inertial frequency, while, in the second case, they are greater. The intense wave activity observed in the regions of oceanic fronts and jet currents can be related to the existence of trapped waves.     

夏季长江河口层化与湍流混合特征分析

利用2016年夏季长江河口现场水文特性与湍流微结构观测资料, 分析了长江河口水体温盐结构、层化发育、湍流与混合特征。结果表明: 1)夏季长江河口水体密度层化结构明显, 根据各层水体密度梯度差异, 可将水体分为底部混合层和上层密度跃层, 两部分的密度层化界限与浮力频率等值线lg N ² = - 4.0接近。2)底部混合层湍动能耗散率大, 层化结构弱, 水体分层稳定性弱; 上层密度跃层湍动能耗散小, 层化结构强, 水体分层稳定性强, 这有利于河口内波的发育与传播。3)在密度层化的作用下, 水体的湍动能耗散率、湍动能剪切生成及浮力通量的能量关系在一定范围内符合湍动能局部能量平衡方程。不同层之间的湍流弗劳德数Fr_t和湍流雷诺数Re_t在Fr_t-Re_t平面上呈现明显的分区, 与经典的分层剪切流理论基本吻合。     

Air-Sea Interactions under the Existence of Opposing Swell

Data of a comprehensive laboratory study on the coexistent system of wind waves and opposing swell (Mitsuyasu and Yoshida, 1989) have been reanalyzed to clarify the air-sea interaction phenomena under the coexistence of wind waves and swell. It is shown that the magnitude of the decay rate of swell due to an opposing wind is almost the same as that of the growth rate of swell caused by a following wind, as measured by Mitsuyasu and Honda (1982). The decay rate is much smaller than that obtained recently by Peirson et al. (2003), but the reason for the disagreement is not clear at present. The effect of an opposing swell on wind waves is very different from that of a following swell; wind waves are intensified by an opposing swell while they are attenuated by a following one. The phenomenon contradicts the model of Phillips and Banner (1974), but the reason for this is not clear at this time. The high-frequency spectrum of wind waves shows a small increase of the spectral density. Wind shear stress increases a little due to the effect of opposing swell. The intensification of wind waves by opposing swell and the small increase of the spectral density in a high-frequency region can be attributed to the increase of wind shear stress. Such organized phenomena lead to the conclusion that the hypothesis of local equilibrium for pure wind waves (Toba, 1972) can also be satisfied for wind waves that coexist with opposing swell. The recent finding of Hanson and Phillips (1999) can be explained by this mechanism.     

A New Class of Edge Baroclinic Waves and the Mechanism of Their Generation

Edge baroclinic waves are generated in a geostrophic flow with a vertical shear near a solid surface. The study investigates a new class of baroclinic waves in flows with horizontal and vertical shears and a linear distribution of potential vorticity. It is shown that taking account of the horizontal shear leads to the appearance of new features of wave dynamics. These include the nonmodal growth of energy in the initial stage of development, the time dependence of the vertical wave scale, and the possibility of generation of stationary or blocked waves. The horizontal shear makes the mechanism of generation of baroclinic waves by initial vortex perturbations more efficient. One important feature is associated with vortex paths, which are formed by the superposition of a baroclinic wave on the flow with horizontal shear.     

The influence of quasi resonant internal waves on the radar imaging mechanism of shallow sea bottom topography

During previous field experiments in the North Sea it was often assumed that the water column in such shallow coastal tidal waters is vertically well mixed and stratification was neglected when discussing the Normalized Radar Cross Section modulation caused by the sea floor. In this paper the influence of quasi resonant internal waves with the sea bed on the radar imaging mechanism of submarine sand waves itself is investigated. In situ data of the tidal current velocity and several water quality parameters such as sea surface temperature, fluorescence, and beam transmittance were measured in the Southern Bight of the North Sea in April 1991. Simulations of the total NRCS modulation caused by sand waves and internal waves as a function of the current gradient or strain rate induced by the internal wave current field at the sea surface have been carried out using the quasi-steady approximation and linear internal wave theory. As a first approximation the strain rate depending on stratification was calculated using the two-layer model. These simulations demonstrate that at least a density difference between the two layers of the order of Δρ ≈ 1 kg m^–3 is necessary for a sinusoidal thermocline to effect the total NRCS modulation considerably. The NRCS modulation as a function of wind friction velocity has been calculated independently and is discussed with regard to the strain rate of the surface current field caused by the superimposed imaging mechanisms of sand waves and internal waves. It turned out that the existence of a surface roughness-wind stress feedback mechanism cannot be excluded.     

东海内陆架春季跃层和内波影响下的环境要素分布

基于东海内陆架P2连续站春季流速和环境要素的观测数据,发现该站存在由浙闽沿岸水系和陆架混合水系界面形成的较强跃层,跃层的浮频率在1×10-3s-2左右。跃层上下水体的温盐值变化和流场的变化有相关关系。环境要素在跃层的影响下呈现显著的分层结构,说明跃层对环境要素的垂直交换起到了限制作用。同时跃层的存在也为内波的产生提供了条件,斜压结构主要由具有半日潮频率的内潮和近惯性频率的内波组成。在观测开始和结束时刻,跃层深度显著抬升,跃层中存在Ri-1大于4的情况,这与叶绿素溶解氧跨跃层现象存在的时刻对应,说明这两个时刻水体由于内波活动改变了跃层深度并存在剪切不稳定的情况,进而引起了水体的垂向交换,为环境要素的跨跃层混合提供了条件。跃层和内波分别对环境要素的垂直混合起到了阻碍和加强的作用。     

Downward transfer of momentum by wind-driven waves

A model for the downward transfer of wind momentum is derived for growing waves. It is shown that waves, which grow due to an uneven pressure distribution on the water surface or a wave-coherent surface shear stress have horizontal velocities out of phase with the surface elevation. Further, if the waves grow in the x-direction, while the motion is perhaps time-periodic at any fixed point, the Reynolds stresses associated with the organized motion are positive. This is in agreement with several field and laboratory measurements which were previously unexplained, and the new theory successfully links measured wave growth rates and measured sub-surface Reynolds stresses. Wave coherent air pressure (and/or surface shear stress) is shown to change the speed of wave propagation as well as inducing growth or decay. From air pressure variations that are in phase with the surface elevation, the influence on the waves is simply a phase speed increase. For pressure variations out of phase with surface elevation, both growth (or decay) and phase speed changes occur. The theory is initially developed for long waves, after which the velocity potential and dispersion relation for linear waves in arbitrary depth are given. The model enables a sounder model for the transfer to storm surges or currents of momentum from breaking waves in that it does not rely entirely on ad-hoc turbulent diffusion. Future models of atmosphere-ocean exchanges should also acknowledge that momentum is transferred partly by the organized wave motion, while other species, like heat and gasses, may rely totally on turbulent diffusion. The fact that growing wind waves do in fact not generally obey the dispersion relation for free waves may need to be considered in future wind wave development models.     

Experimental Study on the Bed Shear Stress Under Breaking Waves

The object of present study is to investigate the bed shear stress on a slope under regular breaking waves by a novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor. The sensors were calibrated before application, and then a wave flume experiment was conducted to study the bed shear stress for the case of regular waves spilling and plunging on a 1:15 smooth PVC slope. The experiment shows that the sensor is feasible for the measurement of the bed shear stress under breaking waves. For regular incident waves, the bed shear stress is mainly periodic in both outside and inside the breaking point. The fluctuations of the bed shear stress increase significantly after waves breaking due to the turbulence and vortexes generated by breaking waves. For plunging breaker, the extreme value of the mean maximum bed shear stress appears after the plunging point, and the more violent the wave breaks, the more dramatic increase of the maximum bed shear stress will occur. For spilling breaker, the increase of the maximum bed shear stress along the slope is gradual compared with the plunging breaker. At last, an empirical equation about the relationship between the maximum bed shear stress and the surf similarity parameter is given, which can be used to estimate the maximum bed shear stress under breaking waves in practice.     

Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

The high-resolution vertical structure of internal tides and near-inertial waves measured with an ADCP over the continental slope in the Bay of Biscay

ADCP measurements of the velocity structure in the permanent thermocline at two locations over the continental slope in the Bay of Biscay are presented. The vertical variation of the contribution of the inertia-gravity waveband to the kinetic energy, vertical motion, and current shear are analysed. The semi-diurnal tides together with near-inertial waves appear to provide over 70% of the high-frequency kinetic energy (>1/3 cpd). Over the vertical range of the ADCP observations the phase of the harmonic M₂ tide changes up to 155°, while the kinetic energy varies in the vertical by a factor of 3.8, showing the importance of the contribution of internal waves to the observed tidal motion. Both semi-diurnal internal tidal waves and near-inertial waves have a vertically restricted distribution of the variance of the horizontal and vertical velocity, as in internal wave beams. The short-term 14-day averaged amplitude and phase lag of the M₂ tide shows large temporal changes, with a characteristic 40–45 day time scale. These changes are probably related to variations in generation sites and propagation paths of the internal tide, because of changes in the temperature and salinity stratification due to the presence of meso-scale eddies. The relatively large shear in the inertia-gravity wave band, mainly at near-inertial frequencies, supports low-gradient Richardson numbers that are well below 1 for nearly half of the time. This implies that the large shear may support turbulent mixing for a large part of the time.     

Electromagnetic fields of waves in the sea stratified over density and electrical conductivity

The paper addresses the theoretical problem of electromagnetic fields induced by surface and internal waves in a fluid with continuously stratified electrical conductivity and density. Calculations of the electromagnetic fields induced by the wave motion in the tropical Atlantic have been performed considering the exponentially changing electrical conductivity in the vertical. The consideration of the electrical conductivity stratification is shown to be capable of modifying electromagnetic fields in the individual fluid layers by about 50%, and the role of this stratification is shown to increase with the growth of the wave period. Translated by Vladimir A. Puchkin.     

畸形波作用下半潜浮式风机系泊失效停机响应分析

半潜浮式风机逐渐在深海风电开发中受到关注,建立风机、平台与系泊结构耦合数值计算模型,通过FAST与AQWA链接进行风机塔基荷载及平台运动响应相互耦合传递,基于随机波与极限波组合模型生成畸形波时程序列,进行半潜浮式风机系泊失效全过程时域模拟计算分析,得出系泊锚链张力、风机、塔筒和平台运动时程响应,探究系泊失效、风机停机和叶片变桨速率对浮式风机平台系泊结构动力响应的影响。结果表明：畸形波作用下浮式平台和系泊结构动力响应显著,系泊失效导致塔基剪力增加,平台纵荡和纵摇运动响应显著增大;风机停机会引起系泊锚链张力显著减小,转子推力、塔基剪力和叶尖挥舞位移响应逐渐衰减,平台纵荡、纵摇和横摇运动响应显著减小;随着叶片变桨速率增加,风机转子推力和塔基剪力波动幅值增大。     

Linear dynamics of Eady waves in the presence of horizontal shear

The problem of the instability of the flow of a stratified rotating fluid with constant vertical and horizontal shears is investigated within the framework of a quasi-geostrophic approximation. It is shown that the horizontal shear, when taken into account, leads to a qualitative change in the dynamics of Eady waves, i.e., wave solutions with zero potential vorticity. The main salient feature is related to the effect of the temporary exponential growth of the unstable waves, i.e., the growth effect in a finite time interval. This effect is manifested by an alternation of the stages of a smooth oscillating behavior (in time) with an exponential (explosive) growth of finite duration. A kinematic interpretation of the effect of the temporary exponential growth is suggested which is associated with the passage of a time-dependent wave disturbance vector across the domain of the exponential instability existing in the absence of horizontal shear. Along with the dynamics of individual Eady waves, the generation process of these waves—caused by an initial disturbance defined by one spatial Fourier harmonic—is also investigated. It is shown that this process is accompanied by the formation of nonmodal waves, with time-varying horizontal and vertical wavenumbers and nonzero potential vorticity. The interaction of the nonmodal wave with the background flow leads to an algebraic growth of the Eady wave at the initial cyclogenesis stage.     

Surface manifestations of internal waves investigated by a subsurface buoyant jet: Part 2. Internal wave field

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, a major simulation of internal wave actuation by buoyant turbulent jets generated by wastewater flows from underwater collector diffusers in conditions of temperature stratification with deep and shallow thermocline has been performed. Using a modification of the particle tracing velocimetry (PTV) method in the stratification mode with shallow thermocline, the velocities of currents generated by internal waves at the surface of the water area are measured. A theoretical model is developed describing the fields of internal waves in the presence of jet stream. Dispersion relations and structures of lower (first and second) modes of internal waves in the stratified basin for different rates of liquid outflow from the collector model are obtained. The experimentally measured field of isothermal shifts with respect to the system of characteristic modes of internal waves is decomposed. A mixed regime of internal wave actuation with the simultaneous existence of the first and second modes is observed. The characteristics of perturbations in the liquid column and on its surface are compared. This analysis allows us to prove that the velocity fields on the surface are indeed surface manifestations of internal waves.     

Investigation of Barotropic and Baroclinic Seiches in Bounded Sea Basins

We present a survey of works carried out at the Wave-Theory Department of the Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine for the last ten years and devoted to investigation of free and forced waves in bounded basins. Our attention is focused on the results of investigation of internal waves in basins of variable depth for the case of three-layer stratification of the liquid. The profiles of the bottom of the basin and interfaces are regarded as parabolic. Analytic solutions are obtained and the periods of oscillations of the free surface and interfaces for the first and second modes are determined. The dependences of the characteristics of baroclinic waves on the geometry of the basin and parameters of stratification are analyzed.     

Seabed shear stresses under irregular waves plus current from Monte Carlo simulations of parameterized models

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.     

Floc size variability under strong turbulence: Observations and artificial neural network modeling

The flocculation of cohesive sediment in the presence of waves is investigated using high-resolution field observations and a newly-developed flocculation model based on artificial neural networks. Vertical profiles of suspended sediment concentration and turbulent intensity are estimated using measurements of current profile and acoustic backscatter. The vertical distribution of floc size is estimated using an artificial neural network (ANN) that is trained and validated using floc size measurements at one vertical level. Data analysis suggests a linear correlation between suspended sediment concentration and turbulence intensity. Observations and numerical simulations show that floc size is inversely related to sediment concentration, turbulence intensity and water temperature. The numerical results indicate that floc growth is supported by low concentration and low turbulence. In the vertical direction, mean size of flocs decreases toward the bottom, suggesting floc breakage due to increasing turbulence intensity toward the bed. A significant decrease in turbulent shear could occur within the bottom few-cm, related to increased damping of turbulence by sediment induced density stratification. The results of the numerical simulations presented here are consistent with the concept of a cohesive sediment particle undergoing aggregation-fragmentation processes, and suggest that the ANN can be a precise tool to study flocculation processes.     

Observations of turbulence under weakly and highly stratified conditions in the Ariake Sea

Observations of turbulence, stratification, and mean current were made using a microstructure profiler and an acoustic Doppler current profiler (ADCP) during four cruises at a central location in the Ariake Sea, under weakly and strongly stratified conditions. Continuous measurements of the dissipation rate of turbulent kinetic energy (TKE), ε, were made. These revealed that frictional bed turbulence with quarterdiurnal variation in the bottom boundary layer (BBL) was one of the most energetic sources of vertical mixing in the sea. Thickness of the BBL was strongly confined by the stable stratification. We investigate a relationship between the BBL height h and the Ozmidov scale. We present a systematic argument that describes the vertical structure and characteristic scales of velocity and turbulence inside the frictional BBL, where the stratification persisted. Considerable deviation of observed vertical shear from the law of the wall indicated a modification of turbulent scales by the stratification. Shear stress calculated from the velocity data using vertical integration of the equation of motion was found to decrease approximately linearly with height. The TKE production rate P, estimated using the shear stress, was highly correlated with the dissipation rate. The buoyancy contribution to TKE balance in the BBL was quantified in terms of the flux Richardson number R _f as R _f?=?0.12.     

On the use of a two-layer fluid stratification model in studies of topographically-generated baroclinic tides

Internal waves generated by a baroclinic internal wave impinging on an oceanic ridge are studied. Two stratification models are considered: a two-layer ocean model (with a density jump) and a continuously stratified ocean model (model pycnocline). The results yielded by different stratification models are compared analytically. The analysis makes possible the application of a piecewise-constant approximation of the fluid stratification to study topographically-generated baroclinic tides. Translated by V. Puchkin.